In this paper, we introduce a comprehensive grant-free random access scheme for machine-type communication which is characterized by massive connectivity and low latency. The scheme presented in here is comprehensive in a sense that, synchronization, channel estimation, and users identification & data detection (multi-user detection) are performed all in a single shot. The scheme employs compressive sensing by exploiting two sparse phenomena: sparsity in users activity and sparsity in multi-path channel. Furthermore, the scheme is designed in such a way that channel estimation and multi-user detection have a bi-directional mutual relationship, enabling one to reinforce the other for accurate detection and estimation. Moreover, the iterative order recursive least square (IORLS) estimation algorithm is modified & employed in such a way that it exploits the joint structure in multi-path channel and multi-user signal sparsity.